Vol. 6, No. 2 (2022): Regular Issue

In this paper, two-dimensional nonlinear systems possessing univariate quadratic vector fields with a single-variable only are discussed, and the appearing and switching bifurcations for the 1-dimensional flows (e.g., sink and source flows, and up-parabola and down-parabola flows) will be discussed herein. The upper-saddle and lower-saddle flows are for the appearing bifurcations of the sink and source flows. The increasing-inflection and deceasing-inflection flows are for the appearing bifurcations of the up-parabola and down-parabola flows. The infinite-equilibriums are for switching bifurcations between the sink and source flows and the up-parabola and down-parabola flows. The bifurcations of the 1-dimensional flows are much richer than the bifurcations of equilibriums. The switching of the sink and source flows with parabola flows are very significant in applications, and it can be used to determine flow singularity.

In this paper elastically clamping conditions are given for the bending problem of rectangular plate. It is assumed that these conditions and physical and mechanical properties of the plate material do not depend on temperature. Within the framework of the momentless theory, expressions are obtained for compressive forces, arising as a result of a uniform increase in temperature. A wide range of elastic pinching conditions is considered. In the general case, both a system of differential equations of partial derivatives with unknown variable coefficients and corresponding boundary conditions are obtained to solve the addressed problem. Unknown functions are represented by multiples. A homogeneous system of algebraic equations with respect to unknown coefficients of polynomials is obtained. For certain problems, introducing dimensionless quantities, a technique to calculate the critical temperature by the collocation method is described.

Structures with nonlinear stiffnesses have been proposed for passive vibration isolation to achieve high static stiffness and low dynamic stiffness. Unfortunately, the design of nonlinear structures is very cumbersome because of the nonlinear geometry. Mechanisms with negative stiffnesses have found successful applications in industry. These mechanisms could be included in mechanical vibration courses since the design requires only the linear analysis. However, the stiffnesses of these structures with a compressive load are not available in the literature. This paper provides derivation of the stiffnesses of beam mechanisms with compressive loads. The derivation is based on the solution of the ordinary differential equation in the buckling analysis of columns.

Aiming at the problem of fault phase selection for high-voltage transmission lines, a new method for identifying fault types of transmission lines based on the composite characteristics of fault current combined with support vector machines (SVM) is proposed. First, perform phase-to-mode conversion on the three-phase currents fault component extracted by the measurement unit, and then obtain the Euclidean distance, cosine similarity and Pearson correlation coefficient between the two modulus currents, and finally combine the calculated results in order. Characteristic sample vector to characterize the type of transmission line fault. Then use the powerful pattern recognition capability of the support vector machine to identify the fault type. The simulation results show that the proposed algorithm can accurately identify specific fault types of transmission lines under various working conditions.

We examine the viscous effects of slip boundary conditions for the model describing two-dimensional Navier-Stokes flows in a plane diffuser. It is shown that the velocity profile is related to a half period shifted Weierstrass function with two parameters. This allows to approximate the explicit solution by a Taylor series expansion with two new micro-parameters, that can be measured in physical experiments. It is shown that the assumption for no-slip boundary conditions is stable in the sense that a small perturbation of the boundary values result in a small perturbation in the solutions.